It was observed in [1]} that the matrices \({\bf H}_r\)  defined in (REF ) are similar to \({\bf H}^\prime _r\) 
computed for \({\bf A}^\prime ,{\bf B}^\prime ,{\bf C}^\prime \) , see
(REF ).
The similarity of the two matrices implies that the matrices have the same characteristic polynomial [2]}.
\({\cal P}_r(t)=\mbox{det}(t{\bf I}-{\bf H}_r),\qquad t\in {\bf R}~.\) 
